On data-based estimation of possibility distributions

Abstract

In this paper, we show how a possibilistic description of uncertainty arises very naturally in statistical data analysis. In combination with recent results in inverse uncertainty propagation and the consistent aggregation of marginal possibility distributions, this estimation procedure enables a very general approach to possibilistic identification problems in the framework of imprecise probabilities, i.e. the non-parametric estimation of possibility distributions of uncertain variables from data with a clear interpretation.